Skip to main content
SpringerLink
Log in

Almost nilpotent varieties with non-integer exponents do exist

  • Brief Communications
  • Published:
Moscow University Mathematics Bulletin Aims and scope

Abstract

The existence of an almost nilpotent variety of linear algebras with noninteger exponent is proved. Examples of almost nilpotent varieties with integer exponents were only known so far.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. A. Giambruno and M. Zaicev, Polynomial Identities and Asymptotic Methods, Math. Surveys and Monogr. Vol. 122 (Amer. Math. Soc., Providence, RI, 2005).

  2. Yu. Yu. Frolova and O. V. Shulezhko, “Almost Nilpotent Varieties of Leibniz Algebras,” Prikl. Diskr. Matem., No. 2(28), 30 (2015).

    Google Scholar 

  3. S. Mishchenko and A. Valenti “An Almost Nilpotent Variety of Exponent 2,” Isr. J. Math. 199, 241 (2014).

    Article  MathSciNet  MATH  Google Scholar 

  4. O. V. Shulezhko, “New Properties of Almost Nilpotent Variety of Exponent 2,” Izv. Saratov Univ. (N.S.), Ser. Matem. Mekhan. Inform. 14 (3), 316 (2014).

    MATH  Google Scholar 

  5. S. P. Mishchenko and O. V. Shulezhko, “Almost Nilpotent Varieties of Arbitrary Integer Exponent,” Vestnik Mosk. Univ., Matem. Mekhan., No. 2, 53 (2015). [Moscow Univ. Math. Bull., 70 (2), 92 (2015)].

    MathSciNet  MATH  Google Scholar 

  6. S. P. Mishchenko and O. V. Shulezhko, “On Almost Nilpotent Varieties in the Class of Commutative Metabelian Algebras,” Vestnik Samar. Gos. Univ., Estest. Nauch. Ser. No. 3(125), 21 (2015).

    MATH  Google Scholar 

  7. O. V. Shulezhko, “Almost Nilpotent Varieties in Different Classes of Linear Algebras,” Chebyshevskii Sborn. 16 (1), 67 (2015).

    MathSciNet  Google Scholar 

  8. M. V. Zaicev and S. P. Mishchenko, “On the Colength of Varieties of Linear Algebras,” Matem. Zametki 79 (4), 553 (2006). [Math. Notes, 79 (3–4), 511 (2006)].

    Article  MathSciNet  Google Scholar 

  9. A. Giambruno, S. Mishchenko, and M. Zaicev, “Codimensions of Algebras and Growth Functions,” Adv. Math. 217, 1027 (2008).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ulyanovsk State University, Faculty of Mathematics, Informatics, and Aviation Technologies, ul. L. Tolstogo 43, Ulyanovsk, 432970, Russia

    S. P. Mishchenko

Authors
  1. S. P. Mishchenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. P. Mishchenko.

Additional information

Original Russian Text © S.P. Mishchenko, 2016, published in Vestnik Moskovskogo Universiteta, Matematika. Mekhanika, 2016, Vol. 71, No. 3, pp. 42~46.

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Mishchenko, S.P. Almost nilpotent varieties with non-integer exponents do exist. Moscow Univ. Math. Bull. 71, 115–118 (2016). https://doi.org/10.3103/S0027132216030062

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0027132216030062

Search

Navigation